Standard #: MA.912.C.3.8


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Find average and instantaneous rates of change. Explain the instantaneous rate of change as the limit of the average rate of change. Interpret a derivative as a rate of change in applications, including velocity, speed and acceleration.


Examples


Example: The vertical distance traveled by an object within the earth’s gravitational field, neglecting air resistance, is given by the equation x=0.5gt2 + vot + xo, where g is the force on the object due to earth's gravity, vo is the initial velocity, x0 is the initial height above the ground, t is the time in seconds and down is the negative vertical direction. Determine the instantaneous speed and the average speed for an object, initially at rest, 3 seconds after it is dropped from a 100 m. tall cliff. Describe the object 5 seconds after it is dropped from the same height. Use begin mathsize 12px style g space equals negative 10 m over s squared end style.

General Information

Subject Area: Mathematics (B.E.S.T.)
Grade: 912
Strand: Calculus
Standard: Apply derivatives to solve problems.
Date Adopted or Revised: 08/20
Status: State Board Approved

Related Courses

Course Number1111 Course Title222
1202300: Calculus Honors (Specifically in versions: 2014 - 2015, 2015 - 2022, 2022 and beyond (current))


Related Resources

Perspectives Video: Expert

Name Description
Velocity of the Aucilla River

Harley Means discusses the mathematical methods hydrologists use to calculate the velocity of rivers.

Download the CPALMS Perspectives video student note taking guide.

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